The present disclosure relates to wireless communication systems, and more particularly to transmission diversity in orthogonal frequency division multiplexing systems.
Demand for wireless digital communication and data processing systems is on the rise. Inherent in most digital communication channels are errors introduced when transferring frames, packets or cells containing data over a channel that has some characteristics. Such errors are often caused by interference or thermal noise. The bit error rates of wireless transmission systems pose certain difficulties in designing encoding and decoding schemes for data to be transmitted via such systems. Partly because of its mathematical tractability and partly because of its application to a broad class of physical communication channels, the additive white Gaussian noise (AWGN) model is often used to characterize the noise in most communication channels.
One type of wireless communication system is an Orthogonal Frequency Division Multiplexed (OFDM) system. OFDM is a multi-carrier modulation technique that partitions the overall system bandwidth into multiple (N) orthogonal frequency subcarriers. These subcarriers may also be called tones, bins, and frequency channels. Each subcarrier may be modulated with data. Up to N modulation symbols may be sent on the N total subcarriers in each OFDM symbol period. These modulation symbols are converted to the time-domain with an N-point inverse fast Fourier transform (IFFT) to generate a transformed symbol that contains N time-domain chips or samples.
To improve transmission diversity, space-time block coding in each of the two transmission paths has been developed, as described in Alamouti, “Space-Time Block Coding, A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Selected Areas in Communications, Volume 16, pp. 1451-1458, October 1998, the content of which is incorporated herein by reference in its entirety. The channel is assumed to be time/frequency invariant (flat) and is further assumed to remain constant over at least two consecutive symbols.
In accordance with the transmission scheme described in Alamouti, the original symbol sequence x(n) is divided into blocks of two consecutive symbols xk(n) and xk+1(n). In Alamouti every pair of symbols is subsequently mapped according to the following:
                                          [                                                                                x                    k                                                                                                                    x                                          k                      +                      1                                                                                            ]                    ⇒                      [                                                                                x                    k                                                                                        -                                          x                                              k                        +                        1                                                                                                                                                              x                                          k                      +                      1                                        *                                                                                        x                    k                    *                                                                        ]                          =        ℵ                            (        1.1        )            where for simplicity, time-index n is not included in expression (1.1)
Symbols xk and xk+1* are transmitted at time k respectively from the first and second transmit antennas. Symbols −xk+1 and xk* are transmitted at time k+1 respectively from the first and second transmit antennas. The corresponding received signal rk, rk+1 at times k and k+1 are defined by the following expressions:rk=xkh1+xk+1*h2+nk rk+1=−xk+1h1+xk*h2+nk+1  (1.2)where h1 and h2 respectively represent the channels associated with the first and second transmission paths, and are further assumed to be constant over two symbol periods. The received signals rk, rk+1 may be written as follows:
                                                                                          r                  k                                ⁢                                  •                  ⁡                                      [                                                                                                                        r                            k                                                                                                                                                                            r                                                          k                              +                              1                                                        *                                                                                                                ]                                                              =                                                                    [                                                                                                                        h                            1                                                                                                                                -                                                          h                              2                                                                                                                                                                                                        h                            2                            *                                                                                                                                h                            1                            *                                                                                                                ]                                    ⁡                                      [                                                                                                                        x                            k                                                                                                                                                                            x                                                          k                              +                              1                                                                                                                                            ]                                                  +                                  [                                                                                                              n                          k                                                                                                                                                              n                                                      k                            +                            1                                                    *                                                                                                      ]                                                                                                        =                                                H                  ·                                                            x                      ~                                        k                                                  +                                                      n                    ~                                    k                                                                                        (        1.3        )            
It is understood that the channel matrix H is orthogonal and that an optimum receiver for this transmit diversity scheme multiplies rk by H*, which is the matched filter receiver, to get two decision statistics for xk and xk+1, i.e., to recover the transmitted symbols. Using this method, a diversity order of two is achieved at a receiver with a single receive antenna.
The method described above may be adapted for use in OFDM systems by replacing the time-domain computations with frequency-domain computations. Assume Xn and Xn+1 are two OFDM symbols to be transmitted on sub-carriers n and n+1 in an OFDM system. In addition, for each transmit antenna m assume the channel remains constant over two consecutive sub-carriers. That isHm,n≈Hm,n+1=Hm  (1.4)
By replacing the time-domain computations with frequency-domain computations, the received signal vector corresponding to sub-carriers n and n+1 may be written as:
                                          R            k                    ⁢                      •            ⁡                          [                                                                                          R                      k                                                                                                                                  R                                              k                        +                        1                                            *                                                                                  ]                                      =                                            [                                                                                          H                      1                                                                                                  -                                              H                        2                                                                                                                                                        H                      2                      *                                                                                                  H                      1                      *                                                                                  ]                        ⁡                          [                                                                                          X                      k                                                                                                                                  X                                              k                        +                        1                                            *                                                                                  ]                                +                      [                                                                                V                    k                                                                                                                    V                                          k                      +                      1                                        *                                                                        ]                                              (        1.5        )            thus achieving a diversity of 2.
FIG. 1 is a block diagram of a portion of an OFDM transmitter 10 described above. Each OFDM symbol of size N is divided into N/2 groups of symbol pairs [Xn Xn+1]. Each such pair of symbols is then encoded by the space-frequency encoder 12 to generate two different pairs of symbols [Xn−Xn+1] and [Xn+1* Xn*]. Symbol pairs [Xn−Xn+1] are grouped into an N—symbol vector that is supplied to an inverse fast Fourier transform (IFFT) 18 block, which in response, generates an associated time-domain vector x1 that is transmitted from antenna 14. Similarly, symbol pairs [Xn+1*, Xn*] are grouped into another N—symbol vector that is supplied to IFFT 20 block, which in response, generates an associated time-domain vector x2 that is transmitted from antenna 16.
As is seen from FIG. 1 and described above, the space-frequency encoding is performed on the input symbols, i.e., in the frequency domain. Accordingly, space-encoder 12 is required to generate two different streams and hence two separate IFFT blocks 18, 20, each associated with a different transmit antenna, are required for every transmitted OFDM symbol.